Method for avoiding image occlusions in nuclear magnetic resonance tomography apparatus that are operated with multi-echo sequences

ABSTRACT

In a method for avoiding image occlusions in nuclear magnetic resonance tomography apparatus that are operated with multi-echo sequences, at a time t 0 , a cross-magnetization in spins is generated in an examination subject with an excitation radio-frequency pulse. At times t 1 , t 3 , t 5  . . . , at least two refocusing radio-frequency pulses that re-phase the cross-magnetization follow and read-out intervals follow at times t 2 , t 4 , t 6  . . . The following condition is satisfied in at least one direction for the gradients G activated during the pulse sequence: ##EQU1## Even given quadratic gradient terms, thus, no phase difference occurs between a primary and a stimulated echo path. The presence of such a phase difference causes an image occlusion, and thus such occlusions are avoided by eliminating such a phase difference.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The invention is directed to a method for avoiding image occlusions inthe production of images using a nuclear magnetic resonance tomographyapparatus are operated with multi-echo sequences of the type wherein across-magnetization of spins is generated in an examination subject at atime to with an excitation radio-frequency pulse, this excitationradio-frequency pulse being followed at times t₁, t₃, t₅, . . . by atleast two refocusing radio-frequency pulses that re-phase thecross-magnetization, and read-out intervals following at times t₂, t₄,t₆, . . .

2. Description of the Prior Art

Imaging sequences known as multi-echo sequences that have the followingfeatures in common. A first radio-frequency pulse (excitationradio-frequency pulse) generates a cross-magnetization. At least twofurther radio-frequency pulses (radio-frequency refocusing pulses) thatfollow the radio-frequency excitation pulse re-phase thiscross-magnetization and thus generate measurable MR signals triggered bythe first pulse. For example, these MR signals can be phase-encoded inthe same way, so that the relaxation of the nuclear magnetic resonancesignal can be observed or the signal-to-noise ratio can be approved byaveraging. It is more standard in modern applications, however, toselect a different phase-encoding of the MR signals generated followingthe excitation radio-frequency pulse, so that the data acquisition forthe reconstruction of a MR image becomes faster. Such methods arereferred to as turbo-spin echo sequences. A measuring time that isshortened further is achieved when, following every refocusingradio-frequency pulse, the read-out gradient is also multiply reversed,and thus a plurality of signals are respectively acquired. Such a pulsesequence as disclosed in U.S. Pat. No. 5,270,654 is referred to as agradient spin echo sequence.

It is known that a switched, linear magnetic field gradient asinherently required for the MR imaging cannot be generated isolated in abasic field. On the contrary, switched magnetic field gradients arealways connected to transverse field components as a result of theMaxwell equations. This problem is discussed in a number of references.

D. G. Norris "Phase Errors in NMR Images", SMRM Abstracts 1985, pp.1037-1038 points out the problem of phase distortions due to anundesirable gradient component in conjunction with the traditionalspin-warp technique. For solving this problem, it is proposed that onebipolar pulse be replaced by two mono-polar pulses separated by a 180°radio-frequency pulse.

The problem that has been presented is primarily discussed inconjunction with echo planar imaging (EPI) in the literature. This stemsfrom the fact that the undesired effect becomes more disturbing as thegradient amplitude becomes higher in relationship to the basic magneticfield. Especially short, and thus high, gradients are required, however,in the EPI method. The following solutions have thereby been proposed.

R. Coxon and P. Mansfield "EPI Spatial Distortion in Non-TransversePlanes", SMRM Abstracts 1989, p. 361 propose that the spatial distortioncaused by undesired gradient components be eliminated byafter-processing in the acquired data sets or by dynamic adjustment ofshim currents.

D. G. Norris and J. Hutchinson "Concomitant Magnetic Field Gradients andTheir Effects on Imaging at Low Magnetic Field Strength", MagneticResonance Imaging, Vol. 8, pp. 33-37, 1990, propose for spin echoes, theuse of bipolar pulses as applied, for example, for refocusing givenflux, be replaced by using unipolar pulses. These unipolar pulses areseparated by a 180° radio-frequency pulse, so that they have the effectof a bipolar pulse.

R. M. Weisskoff et al. "Nonaxial Whole-Body Instant Imaging" MRM 29, pp.796-803 (1993) suggest inserting a pre-phasing gradient between a 90°pulse and a 180° for the reduction of phase errors in a EPI pulsesequence.

None of these references, however, is concerned with multi-echo imaging.It has been found that occlusions occur in the image given multi-echosequences, particularly when the gradient field strength is high incomparison to the basic field strength. The problem thus becomesespecially serious given low basic field strengths and/or stronggradients.

SUMMARY OF THE INVENTION

It is an object of the present invention to provide a method of the typeinitially described wherein these occlusions are avoided.

The above object is achieved in accordance with the principles of thepresent invention in a method for operating a nuclear magnetic resonancetomography apparatus, so as to avoid image occlusions, wherein nuclearspins are excited in an examination subject at a time t₀ with aexcitation radio-frequency pulse, the radio-frequency pulse is followedat times t₁, t₃, t₅ . . . by at least two refocusing radio-frequencypulses to re-phase the cross-magnetization, wherein gradients areactivated during the sequence which satisfy the following condition inat least one direction: ##EQU2## wherein n is a natural number, andwherein the resulting nuclear magnetic resonance signals are read-out attimes t₂, t₄, t₆ . . .

DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a conventional multi-echo pulse sequence with aslice-selection gradient GS activated in the standard way and theassociated phase curves for liner and quadratic gradient terms forexplaining the problem to which the inventive method is directed.

FIG. 2 shows a multi-echo pulse sequence with a modified pulse patternfor the slice-selection gradient GS as a first exemplary embodiment ofthe invention.

FIG. 3 shows a multi-echo pulse sequence with a conventionally activatedread-out gradient GR.

FIG. 4 shows a multi-echo pulse sequence with a pulse pattern for aread-out gradient as second exemplary embodiment of the invention.

FIG. 5 shows a multi-echo pulse sequence with a conventional switchingpattern for the read-out gradient GR.

FIG. 6 shows a multi-echo pulse sequence with a switching pattern forthe read-out gradient GR according to a third exemplary embodiment ofthe invention.

FIG. 7 shows a multi-echo pulse sequence with a conventionally activatedpphase-encodinggradient GP.

FIG. 8 shows a multi-echo pulse sequence with a switching pattern forthe pphase-encodinggradient GP according to an exemplary embodiment ofthe invention.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

For explaining the problem to which the inventive method, the occurrenceof transverse field components given activated magnetic field gradientsshall be explained first with reference to the Maxwell equation. It isassumed in the following considerations that a Cartesian coordinatesystem is selected with its z-axis in the direction of the principalmagnetic field. A gradient G having the field components B_(x), B_(y)and B_(z) generates the following magnetic field B in conjunction withthe basic magnetic field B₀ at point x, y, z:

    B=(B.sub.0 +B.sub.z)e.sub.z +B.sub.x e.sub.x +B.sub.y e.sub.y (1)

wherein e_(x), e_(y), e_(z) are unit vectors in the respectivedirections. The absolute value of B is relevant for the MR imaging:##EQU3##

For low gradient fields, only the two first terms B₀ and B_(z) arenormally taken into consideration, these describing the uniform basicfield in combination with the linear field gradient. For gradients thatare strong in relationship to the basic magnetic field, the terms of thesecond order can no longer be left out of consideration. The followingderives from the Maxwell equations for the x-gradient having thestrength G_(x) : ##EQU4##

This means that an x-gradient generates a quadratic field-dependency ofthe second order in the z-direction. A similar result derives for ay-gradient having the strength G_(y) : ##EQU5##

Given the assumption of a cylindrical symmetry, the following derivesfor a z-gradient having the strength G_(z) : ##EQU6##

This means that a z-gradient in the radial direction generates aquadratic term.

The aforementioned, undesired quadratic terms occur in all systemsregardless of the gradient coil design and are especially disturbinggiven low-field systems and given high gradients.

It has been found that the aforementioned quadratic terms in multi-echosequences lead to interferences that represent the cause for theocclusions that have been observed. This is explained in greater detailbelow with reference to FIG. 1.

FIG. 1 shows a conventional multi-echo sequence, whereby only the sliceselection gradient GS of the required gradients is considered here.

At the beginning of the sequence, a radio-frequency excitation pulse RF1is emitted initially under a positive gradient GS1. The nuclear spinsare thereby deflected by 90°, i.e., a cross-magnetization is generated.The phase curve due to the (desired) linear terms of the slice-selectiongradient GS1 are referenced φ1, and φ2 references the phase curve due toquadratic terms. As may be seen, the phase φ1 as well as the phase φ2increases in the second half (reference 1) of the slice-selectiongradient GS1. For re-phasing, a negative gradient G2 is activated underwhich, however, only a re-phasing of the φ1 term ensues, whereas the φ2term continues to increase.

At time t₁, a refocusing radio-frequency pulse RF2 is emitted to thespins, again under the influence of a slice-selection gradient GS3. Itthereby must be taken into consideration that this pulse, as a result ofa non-ideal 180° rotational angle, not only reverses the existingcross-magnetization but also initiates the generation of a stimulatedecho. The phase in the stimulated echo path is indicted with dots inFIG. 1. In the primary echo path, the phase initially increases withrespect to the term φ1 as well as with respect to the term φ2 in thefirst half 3 of the slice-selection gradient GS3 and is then inverted.The phase relation for both terms φ1, φ2 remains present in thestimulated path.

At time t₂, a spin echo system S1 arises, as a purely primary echohaving the overall phase φ(S1): ##EQU7##

A further refocusing radio-frequency pulse under the influence of aslice-selection gradient GS4 follows at time t₃. Here, the phaserelation is inverted not only in the primary echo path but also in thestimulated echo path, with respect to the linear gradient terms as wellas with respect to the quadratic terms. A second spin echo S2 thusarises at time t₄.

This second spin echo S2 and all following spin echoes represent asuperimposition of primary and stimulated echoes with various phaserelations. The phase relation for the primary component, referenced withthe superscript "p", is: ##EQU8## The phase relation of the stimulatedcomponent, referenced with a superscript "s", is: ##EQU9## These phasesmust be identical for a correct echo superimposition:

    φ.sup.s (S2)=φ.sup.p (S2)                          (16)

This condition--as may also be seen from the curve of φ₁ according toFIG. 1--is met φ₁ ^(p) -φ₁ ^(s) =0 for linear gradient terms. When,however, the terms of the second order according to equations 6, 7 and12 are taken into consideration, the condition is not met. These termslead to location-dependent phase differences between the various echotypes. In the worst case, the superimposition of two echo types leads toa quenching when the phase difference becomes equal to π. ##EQU10##

When, for example, G_(x) is the slice-selection gradient, B(t) isobtained from equation 6. When the terms of the second order areconsidered, the phase difference φ₂ ⁰ -φ₂ ^(s) of the terms of thesecond order illustrated in FIG. 1 are obtained as follows: ##EQU11##

The following parameters are assumed in the following example:

Pulse duration of sub-pulses 1-6, according to FIG. 1=2.4 ms

Gradient strength |G_(x) |=7.0 mT/m

For a low-field system having a basic field strength of 0.2 T, thefollowing is obtained at the position |z|=10 cm: ##EQU12## This meansthat a destructive interference of primary and stimulated echoes withstrong signal loss occurs at the position |z|=10 cm.

It has thus been perceived that the interference connected with thegradient terms of the second order represents the cause for imageocclusions in multi-echo sequences.

The destructive interference at time t₄, i.e., with respect to the spinecho S2, however, can be avoided by adhering to the following conditionfor the respective gradient G: ##EQU13##

This condition is valid for all gradient directions since--as derivesfrom equations 6, 7 and 12--the same dependency of G² exists in allspatial directions. Similar conditions must be met for all followingechoes S2, S3, S4 . . . Sn, so that the following general condition isobtained: ##EQU14##

FIG. 2 shows an exemplary embodiment of a pulse sequence wherein thecondition according to equation 21 is met for the slice-selectiongradient G_(s). The difference compared to the pulse sequence of FIG. 1is that the sub-pulse 2 does not, as in FIG. 1, follow theslice-selection gradient G_(S1), or the sub-pulse 1 thereof, but insteadfollows the slice-selection gradient G_(S3), or the sub-pulse 4 thereof.Further, identical slice-selection pulses 2 are attached symmetricallyat both sides of the following slice-selection gradient G_(s). As may beseen from the curve of the phase φ₂ shown in FIG. 2, the phasedifference φ₂ ^(p) -φ₂ ^(s) between the φ₂ terms of the stimulated echoand the primary echo becomes 0, so that a constructive interferenceoccurs.

The above considerations referred only to the slice-selection gradient.In practice, this leads to the largest interference since read-outgradients and phase-encoding gradients are usually smaller. The pulsesequence can also be selected such for these gradients, however, if thecondition according to equation 21 is met.

The phase-relationships for a read-out gradient GR are explained belowwith reference to FIGS. 3-6. FIG. 3 shows a conventionally activatedread-out gradient GR. A gradient pulse GR1 is emitted in the read-outdirection between the excitation radio-frequency pulse RF1 and the firstrefocusing radio-frequency pulse RF2; this gradient pulse GR1 shouldhave a scaled length 1 and a scaled height 3 in the exemplaryembodiment. The first spin echo S1, just like all following spin echoes,is read out under a read-out gradient GR having the scaled height 1 andthe scaled length 2×3. As may be seen from the illustrated phase curvefor the linear gradient terms, the spin echo signal S1 derives from arefocusing of the primary echo; stimulated echoes are also refocused inthe following spin echoes. No phase equality occurs, however, withrespect to the quadratic gradient terms. When the values assumed for thegradient GR are introduced into equation 21, then one can see: ##EQU15##Equation 21 is thus not satisfied. The phase difference φ₂ ^(p) -φ₂ ^(s)that can lead to a destructive interference occurs given echo signal S2.

This, for example, can be avoided by making the first gradient GR1longer, according to FIG. 4, whereby it has a scaled height 1 and scaledlength 3 in the exemplary embodiment. The phase curve φ1 with respect tothe linear gradient term φ1 thereby remains substantially unmodified;the rise steepness under the gradient GR1 merely becomes less. Withrespect the quadratic gradient term, however, only the same phaserotation under the gradient GR is achieved as with respect to the lineargradient term. The condition according to equation 21 is thus met:##EQU16##

As shown in FIG. 4, this results therein that no phase differencebetween the primary echo and the stimulated echo in spin-echo S2 as wellas in the following spin echoes:

    φ.sub.2.sup.p -φ.sub.2.sup.s =0

A constructive superimposition of the two signal terms thus ensues.

FIG. 5 shows a further exemplary embodiment of a conventional read-outgradient GR. In this case, the read-out gradient here is symmetrical tothe respectively allocated echo time and has negative pulses at bothsides thereof. In the exemplary embodiment, the positive part of eachend of a read-out gradient has a scaled length of 2×2 and a scaledheight of 1; the negative pulses respectively have a scaled length of 2and a scaled height of -1. As the illustration of the phase φ1 shows,the phase deriving from the linear gradient re-phases exactly at theecho times with respect to the primary as well as with respect to thestimulated echoes. With respect to the quadratic gradient terms,however, a phase difference φ₂ ^(p) -φ₂ ^(s) is present, for example atthe time of the spin echo S2, between the primary and the stimulatedecho path. Equation 21 is not satisfied, since ##EQU17## Destructiveinterferences with signal quenching thus occur again.

FIG. 6 shows an example of how the phase difference between thestimulated echo and the primary echo can be avoided given this sequencetype. In the illustrated exemplary embodiment, the positive part of theread-out gradient GR is extended to the length 2×3 given unalteredamplitude 1; the negative sub-pulses, by contrast, are shortened to thelength 1 given an unaltered amplitude -1. A positive gradient pulse GRhaving a scaled length 1 and a scaled height 2 is inserted between theexcitation radio-frequency pulse RF1 and the first refocusingradio-frequency pulse RF2. With respect to the linear gradient term, theprimary and the stimulated echo path again coincide beginning with thesecond spin echo S2. Differing from the conventional sequence of FIG. 5,however, the condition according to equation 21 is satisfied here, forexample, at the second spin echo S2: ##EQU18## thereby valid is:

so that φ₂ ^(p) -φ₂ ^(p) =0, i.e., primary and stimulated echo areconstructively superimposed.

FIGS. 7 and 8, also show an example of a phase-encoding gradient GP.Every spin echo S1, S2 . . . is thereby differently phase-encoded with aphase-encoding gradient advanced step-by-step. The step-by-step advanceis indicated in FIG. 7 by the lines in the gradient GP. After every spinecho S1, S2 . . . , the phase coding is in turn reset by a gradienthaving the same amplitude but the opposite direction. A consideration ofthe phase curves φ1 and φ2 for the respective stimulated and primaryecho paths also shows here that conventional pulse sequences in thephase-encoding direction lead to a phase difference between primary andstimulated echo with respect to the quadratic gradient terms, and thusproblems with image quality can occur.

An exemplary embodiment of a solution of this problem with respect tothe pphase-encodingdirection is shown in FIG. 8. A bipolar gradient inthe phase-encoding direction is thereby inserted between the excitationradio-frequency pulse RF1 and the first refocusing radio-frequency pulseRF2. Further, every phase-encoding pulse is bipolar, just like there-phasing pulses inserted after the spin echoes. The conditionaccording to equation 21 can be satisfied with such a pulse sequence, sothat the phase deviations between primary and stimulated echo pathsbecome 0 given quadratic gradient terms as well.

It must be emphasized that the illustrated gradient sequences representonly some of many possibilities for satisfying the condition accordingto equation 21, and thus for avoiding interferences and the imageocclusions connected therewith. This principle can likewise be appliednot only to the illustrated turbo-spin echo sequence but--as initiallyrecited--to any arbitrary multi-echo sequence.

Although modifications and changes may be suggested by those skilled inthe art, it is the intention of the inventors to embody within thepatent warranted hereon all changes and modifications as reasonably andproperly come within the scope of their contribution to the art.

We claim as our invention:
 1. A method for avoiding image occlusions ina nuclear magnetic resonance tomography apparatus operated with amulti-echo sequence comprises the steps of:generating across-magnetization of spins in an examination subject at a time t₀ withan excitation radio-frequency pulse, resulting in nuclear magneticresonance signals in said examination subject; emitting at least tworefocusing radio-frequency pulses following said excitationradio-frequency pulse at time t₁,t₃,t₅ . . . to re-phase thecross-magnetization; activating gradients G(t) which satisfy thefollowing condition in at least one direction: ##EQU19## wherein n is anatural number; reading out the resulting nuclear magnetic resonancesignals at times t₂,t₄,t₆ . . .
 2. A method as claimed in claim 1wherein the step of activating gradients G(t) comprises activating saidgradients G(t) which satisfy said condition in all spatial directions.3. A method as claimed in claim 1 comprising the additional stepsof:emitting each excitation radio-frequency pulse and each refocusingradio-frequency pulse in the presence of a slice-selection gradient;following the slice-selection gradient for a first refocusingradio-frequency pulse with a further gradient in a slice-selectiondirection, said further gradient having an amplitude equal to anamplitude of the slice-selection gradient for the excitationradio-frequency pulse and having a duration which is half as long;andpreceding and following each subsequent slice-selection gradient witha gradient identical to said further gradient.
 4. A method as claimed inclaim 1 wherein the step of reading out the resulting nuclear magneticresonance signals comprises reading out the resulting nuclear magneticresonance signals under a read-out gradient having a duration T and anamplitude A, and comprising the additional step of generating apre-phasing pulse in a read out direction between the excitationradio-frequency pulse and a first refocusing radio-frequency pulse, saidpre-phasing pulse having an amplitude A and a duration T/2.
 5. A methodas claimed in claim 1 wherein the step of reading out the resultingnuclear magnetic resonance signals comprises reading out the resultingnuclear magnetic resonance signals under a read out gradient having aduration T and an amplitude A defining a duration/amplitude product, andcomprising the additional steps of:activating an inverse read-outgradient preceding and following each read-out gradient, with a sum ofthe duration/amplitude products of the respective inverse read-outgradients preceding and following a read-out gradient being less thanthe duration/amplitude product of that read-out gradient; and emitting apre-phasing pulse in a read-out direction between the excitationradio-frequency pulse and a first refocusing radio-frequency pulse, saidpre-phasing pulse having a duration/time product selected so that saidcondition is met for all of the gradients in the read-out direction. 6.A method as claimed in claim 1 comprising the additional stepsof:generating a first bipolar phase-encoding gradient before eachnuclear magnetic resonance signal, said first phase-encoding gradienthaving a duration and an amplitude defining a duration/amplitudeproduct, and increasing said duration/amplitude product step-by-step foreach first phase-encoding gradient from nuclear magnetic resonancesignal-to-nuclear magnetic resonance signal; generating a second bipolarphase-encoding gradient, having an opposite direction to said firstphase-encoding gradient and a same duration/amplitude product, aftereach nuclear magnetic resonance signal and advancing saidduration/amplitude product of said second phase-encoding gradientstep-by-step from nuclear magnetic resonance signal-to-nuclear magneticresonance signal; emitting a bipolar pre-phasing gradient between theexcitation radio-frequency pulse and a first refocusing radio-frequencypulse; and matching said first and second phase-encoding gradients andsaid bipolar pre-phasing gradient to each other so that said conditionis met.